We study the two-dimensional Euler equations, damped by a linear term and driven by an additive noise. The existence of weak solutions has already been studied; pathwise uniqueness is known for solutions that have vorticity in L∞. In this paper, we prove the Markov property and then the existence of an invariant measure in the space L∞ by means of a Krylov–Bogoliubov’s type method, working with the weak⋆ and the bounded weak⋆ topologies in L∞.
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